Sample size calculation for epidemiologic studies: principles and methods.

Objectives To assess the completeness of reporting of sample size determinations in unpublished research protocols and to develop guidance for research ethics committees and for statisticians advising these committees.Design Review...

The number of samples needed to identify significant effects is a key question in biomedical studies, with consequences on experimental designs, costs and potential discoveries. In metabolic phenotyping studies, sample size determination remains a complex step. This is due particularly to the multiple hypothesis-testing framework and the top-down hypothesis-free approach, with no a priori known metabolic target. Until now, there was no standard procedure available to address this purpose. In this review, we discuss sample size estimation procedures for metabolic phenotyping studies. We release an automated implementation of the Data-driven Sample size Determination (DSD) algorithm for MATLAB and GNU Octave. Original research concerning DSD was published elsewhere. DSD allows the determination of an optimized sample size in metabolic phenotyping studies. The procedure uses analytical data only from a small pilot cohort to generate an expanded data set. The statistical recoupling of variables procedure is used to identify metabolic variables, and their intensity distributions are estimated by Kernel smoothing or log-normal density fitting. Statistically significant metabolic variations are evaluated using the Benjamini-Yekutieli correction and processed for data sets of various sizes. Optimal sample size determination is achieved in a context of biomarker discovery (at least one statistically significant variation) or metabolic exploration (a maximum of statistically significant variations). DSD toolbox is encoded in MATLAB R2008A (Mathworks, Natick, MA) for Kernel and log-normal estimates, and in GNU Octave for log-normal estimates (Kernel density estimates are not robust enough in GNU octave). It is available at http://www.prabi.fr/redmine/projects/dsd/repository, with a tutorial at http://www.prabi.fr/redmine/projects/dsd/wiki.

Power and sample size calculations: A review and computer program

Chapter 53 - Sample size

Quantitative monographic studies systematically use inferential statistical procedures to test hypotheses. For this purpose, sampling procedures and sample sizes need to be adequate for the proposed procedures. The aim of this study was to identify the sample selection methods, as well as the performance and types of calculation to determine the sample size adopted in theses and dissertations developed in a graduate program in the field of Physical Education. Theses and dissertations defended between 2003 and 2013 were obtained through digital repository. Only quantitative studies were included, in which the following issues were analyzed: (1) sample selection criteria; (2) presence of sample calculation; (3) calculation type to estimate sample size. A total of 199 studies were included. Of these, 6% (n=11) used probabilistic methods for sample selection and 3% (n=6) used animal models. As for the accomplishment of sample calculations, 36% (n=72) studies reported having adopted this procedure. Of studies that performed sample calculations, 25% (n=18) used predictive equations, 67% (n=48) considered methods with statistical power as their base, 3% (n=2) used confidence interval, 4% (n=3) did not mention the method and 1% (n=1) was based on the type of statistical test to be used later. Nonprobabilistic sampling methods predominate for the selection of subjects; most studies do not report adopting calculations to estimate sample size and, among those that reported the use, the models that consider statistical power as the main criterion are predominant.

Sample size determination is a critical aspect of biomedical research, as it dictates the number of samples needed for a successful experiment that can yield generalizable results to the broader population. This paper outlines the methodology for calculating sample sizes in various categories of biomedical and clinical research, encompassing cross-sectional surveys, comparative studies, case–control studies, cohort studies, and animal studies. Detailed examples are provided for each category. The determination of an appropriate sample size holds significant importance from scientific, ethical, and resource allocation perspectives. It is noteworthy that research outcomes are often directly influenced by the accuracy of sample size calculations. A robust sample size calculation serves as a cornerstone for researchers, enabling them to draw precise inferences with a high level of precision across a spectrum of biomedical and clinical investigations.

Sample size determination under an exponential model in the presence of a confounder and type I censoring

Background: With an estimated 10.4 million incident tuberculosis (TB) cases in 2015, and the current trajectory of 1.5%/year incidence rate decline, new TB vaccines are urgently needed to help meet the WHO goal of tuberculosis elimination by 2050. However, insufficient epidemiological evidence exists to inform TB vaccine development strategies and to assist clinical trial site selection and design. Research to meet these data needs is critical to accelerate TB vaccine development. To maximise the future impact of new TB vaccines, estimates of the population-level impact of vaccine characteristics and implementation strategies are needed to inform design of TB vaccine target product profiles. To accelerate and de-risk clinical trials, appropriate epidemiological data are required to inform trial site selection, sample size calculations and recruitment strategy. However, data availability at trial sites is limited, and prospective studies are resource-intensive, so new methods are needed to collect appropriate data to inform TB vaccine trial design.
\nTo inform data-driven development strategies for new TB vaccines, the aims of this thesis were to 1) estimate the epidemiological impact of new TB vaccine characteristics and implementation in China to inform design of target product profiles; and 2) to develop a novel epidemiological spatial mapping tool capable of informing clinical trial design for new TB vaccines in low-income, high-burden settings.
\nMethods: A deterministic, age-structured, Mycobacterium tuberculosis transmission model was developed and calibrated to age-stratified epidemiological and demographic data from China. This was employed to estimate the population-level epidemiological impact of new TB vaccines over the 2025-2050 time horizon, through an exploration of potential vaccine characteristics and implementation strategies. 
\nA new methodology for empirical data collection to determine spatial distribution of TB notifications was developed. The electronic PArticipant Locator application (ePAL app) combined 3,243 community-identified points of interest with high resolution satellite maps, within an electronic tablet-based case report form. The app was integrated in to the National Tuberculosis Programme in Blantyre, Malawi, for collection of demographics, health status and coordinates of place of residence for patients ≥18 years initiating TB treatment. Accuracy of ePAL-recorded co-ordinates was evaluated against GPS coordinates obtained at the participant’s place of residence. 
\nResults: Mathematical modelling predicted a shift towards a reactivation-driven, ageing TB epidemic in China by 2050. Vaccines protective against disease, effective post-infection and providing at least 5 years protection were essential for achieving higher levels of impact. Vaccination of older adults provided greater population-level impact than vaccinating adolescents for all equivalent vaccines explored, even if much lower coverage were achieved in older adult vaccination. Recommendations for post-infection vaccines were robust to substantial reductions in efficacy and duration of protection in older adults, whereas for pre-infection vaccines in some of these scenarios adolescent vaccination may be equivalent or preferred. Vaccinating older adults with post-infection vaccines provided substantially higher impact than pre-infection vaccines.
\n1,899 TB patients were registered using ePAL in the 12-month study period, with high patient acceptance (98.7%, 1,899/1,924). ePAL achieved clinic-based collection of patient location of residence accurate to a median of 84 metres (IQR: 35-317 metres) in a high population density urban setting without a municipal address system. Advantages of the ePAL system included real-time availability of high-resolution spatial data, low set up costs, and ease of use by health staff as part of routine TB registration. Data were used to identify areas with high TB burden, potentially suitable for TB vaccine trials.
\nConclusions: The research presented in this thesis informs the development of appropriate TB vaccines and target populations to maximise future population-level impact. A prevention of disease vaccine efficacious post-infection and delivered to older adults would contribute towards maximising population-level impact in China. Adolescent-targeted tuberculosis vaccines are likely to have low impact in ageing, reactivation-driven epidemics like China, which suggests a modification of the current strategic focus on adolescents among certain funders. Clinical trials should assess disease endpoints, include M.tb-infected and older adult populations, and extend beyond the usual 2-3 years follow up. To support design of disease endpoint trials, ePAL may provide an accurate, easily implementable, low-cost tool for identification of areas of high TB burden in settings without addresses.

Some Thoughts About Data Type, Distribution, and Statistical Significance

A sample size with sufficient statistical power is critical to the success of genetic association studies to detect causal genes of human complex diseases. Genome-wide association studies require much larger sample sizes to achieve an adequate statistical power. We estimated the statistical power with increasing numbers of markers analyzed and compared the sample sizes that were required in case-control studies and case-parent studies. We computed the effective sample size and statistical power using Genetic Power Calculator. An analysis using a larger number of markers requires a larger sample size. Testing a single-nucleotide polymorphism (SNP) marker requires 248 cases, while testing 500,000 SNPs and 1 million markers requires 1,206 cases and 1,255 cases, respectively, under the assumption of an odds ratio of 2, 5% disease prevalence, 5% minor allele frequency, complete linkage disequilibrium (LD), 1:1 case/control ratio, and a 5% error rate in an allelic test. Under a dominant model, a smaller sample size is required to achieve 80% power than other genetic models. We found that a much lower sample size was required with a strong effect size, common SNP, and increased LD. In addition, studying a common disease in a case-control study of a 1:4 case-control ratio is one way to achieve higher statistical power. We also found that case-parent studies require more samples than case-control studies. Although we have not covered all plausible cases in study design, the estimates of sample size and statistical power computed under various assumptions in this study may be useful to determine the sample size in designing a population-based genetic association study.

Background: Sample size calculations are an important tool for planning epidemiological studies. Large sample sizes are often required in Mendelian randomization investigations.Methods and results: Resources are provided for investigators to perform sample size and power calculations for Mendelian randomization with a binary outcome. We initially provide formulae for the continuous outcome case, and then analogous formulae for the binary outcome case. The formulae are valid for a single instrumental variable, which may be a single genetic variant or an allele score comprising multiple variants. Graphs are provided to give the required sample size for 80% power for given values of the causal effect of the risk factor on the outcome and of the squared correlation between the risk factor and instrumental variable. R code and an online calculator tool are made available for calculating the sample size needed for a chosen power level given these parameters, as well as the power given the chosen sample size and these parameters.Conclusions: The sample size required for a given power of Mendelian randomization investigation depends greatly on the proportion of variance in the risk factor explained by the instrumental variable. The inclusion of multiple variants into an allele score to explain more of the variance in the risk factor will improve power, however care must be taken not to introduce bias by the inclusion of invalid variants.

Traditional sample size calculations for randomized clinical trials depend on somewhat arbitrarily chosen factors, such as type I and II errors. As an alternative, taking a societal perspective, and using the expected value of information based on Bayesian decision theory, a number of authors have recently shown how to determine the sample size that maximizes the expected net gain, i.e., the difference between the cost of the trial and the value of the information gained from the results. Other authors have proposed Bayesian methods to determine sample sizes from an industry perspective. The purpose of this article is to propose a Bayesian approach to sample size calculations from an industry perspective that attempts to determine the sample size that maximizes expected profit. A model is proposed for expected total profit that includes consideration of per-patient profit, disease incidence, time horizon, trial duration, market share, discount rate, and the relationship between the results and the probability of regulatory approval. The expected value of information provided by trial data is related to the increase in expected profit from increasing the probability of regulatory approval. The methods are applied to an example, including an examination of robustness. The model is extended to consider market share as a function of observed treatment effect. The use of methods based on the expected value of information can provide, from an industry perspective, robust sample size solutions that maximize the difference between the expected cost of the trial and the expected value of information gained from the results. The method is only as good as the model for expected total profit. Although the model probably has all the right elements, it assumes that market share, per-patient profit, and incidence are insensitive to trial results. The method relies on the central limit theorem which assumes that the sample sizes involved ensure that the relevant test statistics are normally distributed. Industry officials should consider the use of expected value of information methods for determining sample sizes for proposed trials. The method also can be used to select, from a number of proposed trials, those which maximize return from a fixed research budget.

Sample size and power determination is the first step in the experimental design of a successful study. Sample size and power calculation is required for applications for National Institutes of Health (NIH) funding. Sample size and power calculation is well established for traditional biological studies such as mouse model, genome wide association study (GWAS), and microarray studies. Recent developments in high-throughput sequencing technology have allowed RNAseq to replace microarray as the technology of choice for high-throughput gene expression profiling. However, the sample size and power analysis of RNAseq technology is an underdeveloped area. Here, we present RNAseqPS, an advanced online RNAseq power and sample size calculation tool based on the Poisson and negative binomial distributions. RNAseqPS was built using the Shiny package in R. It provides an interactive graphical user interface that allows the users to easily conduct sample size and power analysis for RNAseq experimental design. RNAseqPS can be accessed directly at http://cqs.mc.vanderbilt.edu/shiny/RNAseqPS/.

To the Editor:—We write to make the case that the practice of providing a priori sample size calculations, recently endorsed in an Anesthesiology editorial, 1is in fact undesirable. Presentation of confidence intervals serves the same purpose, but is superior because it more accurately reflects the actual data, is simpler to present, addresses uncertainty more directly, and encourages more careful interpretation of results. The clinical trial report 2lauded in the editorial in fact serves to illustrate the drawbacks of sample size calculation as a data analysis tool. The a priori calculation presented is based on assumptions about length of stay (normally distributed with a SD of 4.5 days) that did not hold in the actual data, an analysis (comparison of mean length of stay between two groups by t test) that was not presented, and a sample size that was not attained. It therefore does not help the reader interpret the results, which is the proper goal when reporting on a study that has been completed. The post hoc power calculation presented retains most of these deficiencies, and therefore does not help the reader to assess the strength of evidence against a 1.0-day mean advantage for one treatment versus another. In contrast, a confidence interval for the difference in means would directly address this issue. Although the presence of outliers would require a bootstrapping method 3to obtain a valid confidence interval for a difference in means, this bit of extra effort is certainly worthwhile for the central issue of a study, and in any case, much better than relying on convoluted reasoning with invalid power approximations.Perhaps the worst aspect of reporting sample size or power calculations is that it encourages interpretation of studies’ results based only on P values, in particular the widespread fallacy of interpreting P > 0.05 as proving the null hypothesis. The other article 4cited by the editorial provides a glaring example of this type of reasoning, concluding that reporting of sample size calculations did not change over time in any journal but did increase overall (see their fig. 2). Returning to the clinical trial report, consider the statement that death rates “were similar” in the four subgroups. While this is an accurate characterization of what was actually observed, unsophisticated readers are liable to interpret this (contrary to the authors’ intentions) to mean that the study found strong evidence against any substantial difference in death rates. In fact, the exact 595% confidence interval around the odds ratio for death comparing intravenous versus epidural postoperative analgesia goes from 0.36 to 5.4, which is wide enough to make clear to most readers that this study by itself provides only very weak evidence against a clinically important difference in death rates.We urge reviewers, editors, and quality studies to give authors full credit for providing confidence intervals instead of sample size calculations in reports of completed studies. Indeed, for the reasons illustrated here, it would be best to discourage the practice of using sample size and power calculations as substitutes for more direct assessment of uncertainty using confidence intervals.

Mass spectrometric profiling approaches such as MALDI-TOF and SELDI-TOF are increasingly being used in disease marker discovery, particularly in the lower molecular weight proteome. However, little consideration has been given to the issue of sample size in experimental design. The aim of this study was to develop a protocol for the use of sample size calculations in proteomic profiling studies using MS. These sample size calculations can be based on a simple linear mixed model which allows the inclusion of estimates of biological and technical variation inherent in the experiment. The use of a pilot experiment to estimate these components of variance is investigated and is shown to work well when compared with larger studies. Examination of data from a number of studies using different sample types and different chromatographic surfaces shows the need for sample- and preparation-specific sample size calculations.